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Abstract and Applied Analysis
Volume 2014, Article ID 679131, 13 pages
http://dx.doi.org/10.1155/2014/679131
Research Article

Traveling Waves in a Diffusive Predator-Prey Model Incorporating a Prey Refuge

College of Mathematics and Information Science, Wenzhou University, Zhejiang 325035, China

Received 24 January 2014; Accepted 9 March 2014; Published 24 April 2014

Academic Editor: Weiming Wang

Copyright © 2014 Xiujuan Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We establish the existence of traveling wave solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator-prey model incorporating a prey refuge. By using the shooting argument, invariant manifold theory, and the Hopf bifurcation theorem, we analyze the dynamic behavior of this model in the three-dimensional phase space. Numerical results are also presented to illustrate the theoretical results.